Function: AZER

Purpose. Computes the almost invariant zeros of a system.

Synopsis.

[alzer,jsvd] = azer(sys[,rad[,tol[,zer0]]]);

Description. Almost zeros are local minima of the minimum singular value of the system matrix relative to sys. To decide if the values in alzer are true zeros (minimum equal to zero), relevant almost zeros or irrelevant ``almost zeros'', the user must analyze the values of the local minima (given in jsvd). If the values of almost zeros are far from dominant poles, these values must be ignored (like zeros at infinity). Note that the results might vary from on run to another on account of the fact that the used algorithm is initialized by random high gains.

Input arguments

`sys`	LTI system (see `ss.m`).
`rad`	Radius of a circle around origin in which almost zeros are considered. Default `Rad = 100`.
`tol`	Tolerance to distinguish between almost zeros. Default, `tol = 1e-3`.
`zer0`	Vector of initial values for the search of almost zeros. Such initial values can be selected using `plot_zer`.

Output arguments

`alzer`	Almost zeros.
`jsvd`	Corresponding minimum singular value of system matrix. `jsvd(i)` large Þ `alzer(i)` cannot be considered as a zero.

See also: plot_zer for validation of almost zeros by 3-D plotting.